Maybe, but a court could find that he does not legally meet the qualifications to hold office in the first place.
Quo Warranto does that. This is where the President must prove he is eligible for the office of President.
Congress delegated the power to try a usurper via Quo Warranto to the District Court, Washington, D.C. So in fact, Congress could order the trial of the suspected usurper President Obama held there in District Court, and Obama would have to prove he is eligible for the office he was elected to hold.
We’ve been wasting a lot of time going through regional courts, just not the correct one and using the appropriate process.